WASHINGTON – People who fail a background check trying to buy a gun could face increased risk of prosecution under a bill introduced Monday by Florida Sens. Marco Rubio and Bill Nelson and other lawmakers.

The NICS Denial Notification Act, which had previously been introduced in the House, requires federal authorities to alert state law enforcement within 24 hours when individuals "lie and try" to purchase firearms, according to a release from Rubio's office.

State officials could then decide to prosecute or "keep an eye on these denied individuals for signs of future criminal activity." The Justice Department would have to publish an annual report about prosecutions.

Only 13 states that use NCIS get notified when someone fails a background check, according to Rubio's office.

"In the 37 states and the District of Columbia that rely on the FBI to run some or all of their background checks, state authorities generally are not aware when prohibited persons fail background checks run by the FBI. Individuals who are willing to 'lie and try' to buy a gun may be dangerous and willing to obtain guns through other means," read the release.

"As a result, these states and D.C. lack critical law enforcement intelligence that they could use to try to keep their communities safe."

The legislation is sponsored by Sens. Rubio and Nelson along with Pat Toomey, R-Pa., Chris Coons, D-Del.